Maths gcse question

Please could I have help on this question? I have attached the question and my working below but I do not know what I did wrong?
Thank you!

your last part is wrong
2^p*2^p=4^2p
thus, 4^p(1^p-1)

My assumption is where you have written 2p, you mean 2^p.

If so, I’d assume you are on the right track. Can you try collecting like terms together?

Sorry yes that is what I meant.
So I I grouped the like terms would it not be 2^2p-2^p+1 because -2^p-2^p is the same as that multiplied by 2 so it would be 2^p times 2^1 so 2^p+1 but how would I factorise what is given in the question out?

Start by doing a difference of two squares on N.

Ohh yes I used this method and it works now, I got 2^p+1(2^p/2 -1) Thank you!

I think it should be 2^(p-1) rather than 2^(p/2), but the idea is right.

You could expand and then factorise, but a difference of two squares keeps things factorised and is hinted at in the way the expressions are formed.

Yes sorry thank you!!